Simplify the following expression: $ y = \dfrac{3}{5} + \dfrac{3q - 2}{q + 3} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{q + 3}{q + 3}$ $ \dfrac{3}{5} \times \dfrac{q + 3}{q + 3} = \dfrac{3q + 9}{5q + 15} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{3q - 2}{q + 3} \times \dfrac{5}{5} = \dfrac{15q - 10}{5q + 15} $ Therefore $ y = \dfrac{3q + 9}{5q + 15} + \dfrac{15q - 10}{5q + 15} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{3q + 9 + 15q - 10}{5q + 15} $ $y = \dfrac{18q - 1}{5q + 15}$